Great question! I think it's answerable as an overview, but please know this is only the tip of the iceberg.*
Summary: Yes, we have deficits of certain blood products in certain locations at certain times that affect patient care. However, a small percentage of blood product does expire unused (because it wasn't the right product [see background] in the right place at the right time).
A little background
Donated blood is not usually transfused into a patient as whole blood. Instead, it's broken down into several components which are transfused in different clinical scenarios. The issues of storage and supply are different for each component. The components are:
- Plasma, and derivatives
- Red Blood Cells (RBCs)
- Granulocytes (rarely transfused)
These different components require different storage conditions, so they are separated as soon as possible after donation.
OP's first question:
First, do we ever have a blood deficit, situations where someone who could have been saved in a hospital dies because there wasn't blood to treat them?
Yes. Well, actually your question is impossible to answer. :-) We could never know whether someone could-have-been-saved with a transfusion nor whether someone who received a transfusion would-have-died. Those are hypothetical constructs that are interesting to think about but are not compatible with research.
However, we can ask whether there is evidence that blood supply on a clinical level is limited, for instance:
- doctors are requesting products that aren't available for patients;
- doctors are requesting fewer products than they think would be ideal for a particular patient because of a blood bank shortage;
- elective surgeries are being postponed; or
- blood banks are substituting products that may have a slightly increased risk of complications due to less-than-ideal immune compatibility.
All of these are more nuanced than they seem, but to some degree all do occur.
Quoting from a paper in the journal Transfusion entitled How do I manage a blood shortage in a transfusion service?:
Although there are more than 16 million blood donations per year provided to more than 4 million recipients, blood shortages have recurred for decades [...] twice every year. Anyone with any experience at blood centers or transfusion services is quite accustomed to these expected shortages.
He further notes that this problem is likely to worsen because the requirement for transfusions (all types) is increasing at a rate of 5-7% per year while donations are not matching that increase.
The first thing that happens when there is a blood bank shortage usually involves the Transfusion Medicine specialist in the blood bank having a conversation with every doctor who orders the blood product that is limited. Together they determine whether a smaller amount of product or a deferment in transfusion might be clinically appropriate/acceptable.
The distinction between those last two words —
appropriate|accetable — is the key to whether clinical care is actually being compromised. In many cases, clinicians indeed are requesting product beyond what is recommended in published guidelines, because they feel that the patient's condition warrants it due to some special circumstance. It seems likely that at least a small percentage of the time, the clinician was right, but this can never be proven.
It is also the case that elective surgeries are sometimes postponed for this reason (see chart 8-1, p 43), although it's rare.
Related, if we don't run a deficit then what happens to my excess blood?... is it used for medical research?
Although localized shortages of particular products do occur and are disruptive, it is true that a small percentage of the products expire unused. In the U.S., this was estimated at 14% of supply in 1989 and had fallen to 5.2% in 2011, per a report from the US Dept Health and Human Services, the most recent data available I've found. These are complicated and nuanced data that this format does not allow complete explanation of (and I myself am not completely familiar with), but please read the linked HHS report if interested.
As for what happens to the excess - it's probably discarded, although I can't prove that. Regarding your question about research: In addition to being sub-optimal because it's old, the blood was originally collected from human donors. Such research would be subjected to IRB requirements for protection of human subjects. This would likely require researchers to obtain permission from donors (/subjects) at the time of donation to use the product for research. This may happen in localized settings, but I know of no large-scale project.
* I limit this discussion to the U.S. While I realize the weaknesses — inadequacy, really — of that approach, this is the healthcare system where I was able to locate data, the O.P. is apparently asking about the U.S. situation (Red Cross), and I am most familiar with the clinical situation here. If another answer can offer a more global perspective, please do.